Buczolich, Zoltán and Hanson, Bruce and Rmoutil, Martin and Zurcher, Thomas (2019) On sets where lip f is finite. STUDIA MATHEMATICA, 249 (1). pp. 3358. ISSN 00393223

Text
1708.08220.pdf Download (663kB)  Preview 
Abstract
Given a function f : R > R, the socalled "little lip" function lip f is defined as follows:lip f(x) = lim inf(r SE arrow 0) sup(vertical bar x  y vertical bar <= r) vertical bar f(y)  f(x)vertical bar/r.We show that if f is continuous on R, then the set where lip f is infinite is a countable union of countable intersections of closed sets (that is, an Fsigma delta set). On the other hand, given a countable union E of closed sets, we construct a continuous function f such that lip f is infinite exactly on E. A further result is that, for a typical continuous function f on the real line, lip f vanishes almost everywhere.
Item Type:  Article 

Subjects:  Q Science / természettudomány > QA Mathematics / matematika 
SWORD Depositor:  MTMT SWORD 
Depositing User:  MTMT SWORD 
Date Deposited:  20 Feb 2023 11:53 
Last Modified:  20 Feb 2023 11:53 
URI:  http://real.mtak.hu/id/eprint/159468 
Actions (login required)
Edit Item 